I lived in Southern Ohio my entire life up until 2 years ago and Wayne Nat'l forest is your best bet. It takes up MANY, MANY square miles over 4 or 5 counties. They add new land every year too. You really have to do your homework to find out the new land that is added each year too. You can find a jewel if you look where not many people will know about because they don't bother to check. One thing I can tell you is DON'T go when it's close to shotgun season, Ohio doesn't have a rifle season, because you'll think you just dropped into Deer Hunter Central with campers and tents every square yard. I swear I don't know how they stay out of each others way.
You can definitely get PLENTY of room to be by yourself if you pick Wayne Nat'l though. Some HUGE deer roaming those southern Ohio woods.
Nalajr